Robust Detection and Estimation for Logging While Drilling Monopole Acoustic Data

In this paper, we present methods and strategies for robust detection and slowness estimation of weak compressional (P) and shear (S) waves in borehole sonic logging in noisy environments such as while logging while drilling, by proposing methods for enhancing the semblance used in the slowness time coherence method used in the logging. In this direction our contributions are two fold. First, we propose a novel class of shrinkage estimators in the discrete Radon transform domain derived from data semblance, for waveform de-noising to combat random additive noise and reflections. In this context we also identify necessary and sufficient conditions for the optimality of the proposed estimator. Our second contribution lies in developing a novel method to cancel energy propagating at the slowness of borehole modes, chiefly Stoneley, and to a lesser extent, shear, that significantly lowers the semblance of the weaker head wave arrivals. This approach is based on representing the data using time-frequency compact space-time propagators. Finally, we present an algorithm that combines the space time shrinkage in the discrete Radon transform domain and the proposed interference cancelation strategies for enhanced compressional and shear detection via semblance processing. The algorithm is validated on synthetic data and demonstrated to enhance performance on real logging while drilling field data sets.